PDF《qubits》

ARTICLE Received

16 Jan

2015 | Accepted

18 Mar

2015 | Published

29 Apr

2015 Demonstration of a quantum error detection code using a square lattice of four superconducting qubits A.

D. Co ?rcoles1,*, Easwar Magesan1,*, Srikanth J. Srinivasan1,*, Andrew W. Cross1, M. Steffen1, Jay M. Gambetta1 &

Jerry M. Chow1 The ability to detect and deal with errors when manipulating quantum systems is a fundamental requirement for fault-tolerant quantum computing. Unlike classical bits that are subject to only digital bit-?ip errors, quantum bits are susceptible to a much larger spectrum of errors, for which any complete quantum error-correcting code must account. Whilst classical bit-?ip detection can be realized via a linear array of qubits, a general fault-tolerant quantum error-correcting code requires extending into a higher-dimensional lattice. Here we present a quantum error detection protocol on a two-by-two planar lattice of superconducting qubits. The protocol detects an arbitrary quantum error on an encoded two-qubit entangled state via quantum non-demolition parity measurements on another pair of error syndrome qubits. This result represents a building block towards larger lattices amenable to fault-tolerant quantum error correction architectures such as the surface code. DOI: 10.1038/ncomms7979 OPEN

1 IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to A.C. (email: [email protected]). NATURE COMMUNICATIONS | 6:6979 | DOI: 10.1038/ncomms7979 | www.nature.com/naturecommunications

1 &

2015 Macmillan Publishers Limited. All rights reserved. E rrors are inevitable in any real information processor. Quantum computers are particularly susceptible to errors as quantum systems are highly sensitive to noise effects that can be exotic compared with the simple bit-?ip errors of classical computation. As such, realizing a fault-tolerant quantum computer is a signi?cant challenge that requires encoding the information into a quantum error-correcting code. To add to the dif?culty, direct extraction of the information typically destroys the system, and ancillary syndrome systems must be employed to perform non-demolition measurements of the encoded state. Previous work in nuclei1C3, trapped ions4C6 and superconducting qubits7 has attempted to address similar problems;

however, these implementations lack the ability to perform fault-tolerant syndrome extraction, which continues to be a challenge for all physical quantum computing systems. The surface code (SC)8,9 is a promising candidate to achieve scalable quantum computing due to its nearest-neighbour qubit layout and high fault-tolerant error thresholds10. The SC is an example of a stabilizer code11, which is a code whose state is uniquely de?ned by the measurement of a set of observables called stabilizers. Code qubits in the SC are placed at the vertices of a two-dimensional array and each stabilizer involves four neighbouring code qubits. The SC stabilizers are, therefore, geometrically local and can be measured fault tolerantly with a single syndrome qubit12. Error detection on a lattice of code qubits is achieved through mapping stabilizer operators onto a complementary lattice of syndrome qubits, followed by classical correlation of measured outcomes. Among the syndrome qubits, a distinction is made between bit-?ip syndromes (or Z- syndromes) and phase-?ip syndromes (or X-syndromes). Each code qubit in the SC is coupled with two X-syndrome qubits and two Z-syndrome qubits, and, in turn, each syndrome qubit is coupled with four code qubits. Superconducting qubits have become prime candidates for SC implementation13,14, especially with continuing improvements to coherence times15C17 and quantum gates18. Furthermore, implementing superconducting resonators as quantum buses to realize the circuit quantum electrodynamics architecture permits a straightforward path for building connectivity into a lattice of superconducting qubits14. There are numerous ways of building the SC lattice with superconducting qubits and resonators. Here we employ an arrangement in which each qubit is coupled with two bus resonators and each bus couples with four qubits14. Although previously the engineered dissipation of a resonator has been used to stabilize the entanglement of two superconducting qubits to which it is coupled19, it is of note that here the stabilization is achieved via explicitly mapping code qubit stabilizers onto syndrome qubits. Here we experimentally demonstrate the complete algorithm constituting a quantum error detection code that detects arbitrary single-qubit errors in a non-demolition manner via syndrome measurements. The scheme is implemented in a two-by-two lattice of superconducting qubits that represents a primitive tile for the SC. Stabilizer measurements, ubiquitous to fault-tolerant quantum error-correcting codes, are successfully demonstrated in this work for both bit- and phase-?ip errors on an encoded codeword. The non-demolition nature of the protocol is veri?ed by demonstrating the preservation of the entangled state constituting the codeword through high-?delity syndrome measurements in the presence of an arbitrary applied error. These error detection experiments constitute a key milestone for SC implementation, as our operations now extend into the plane of the two-dimensional surface and we show the ability to concurrently perform bit- and phase-parity checks. Moreover, our results illustrate the ability to build structures of super- conducting qubits, which are not co-linear but latticed while preserving high-?delity operations. Moving forward, on improv- ing the measurement and gate ?delities in these systems, further expanding the lattice will lead to important studies of different error-correcting codes and the encoding of logical qubits, thereby allowing experimental........